Supercharge, Invasion and Mudcake Growth in Downhole Applications
Scrivener Publishing
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Handbook of Petroleum Engineering Series
Series Editor: Wilson C. Chin
Scope: Covering every aspect of petroleum engineering, this new series sets the standard in best practices for the petroleum engineer. This is a must-have for any petroleum engineer in today's changing industry.
About the Series Editor:
Wilson Chin earned his PhD from M.I.T. and his M.Sc. from Caltech. He has authored over twenty books with Wiley-Scrivener and other major scientific publishers, has more than four dozen domestic and international patents to his credit, and has published over one hundred journal articles, in the areas of reservoir engineering, formation testing, well logging, measurement while drilling, and drilling and cementing rheology.
Submission to the series:
Phil Carmical, Publisher Scrivener Publishing (512)203-2236 pcarmical@scrivenerpublishing.com
Publishers at Scrivener
Martin Scrivener (martin@scrivenerpublishing.com) Phillip Carmical (pcarmical@scrivenerpublishing.com)
Supercharge, Invasion and Mudcake Growth in Downhole Applications
by Tao Lu, Xiaofei Qin, Yongren Feng, Yanmin Zhou and Wilson Chin
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Library of Congress Cataloging-in-Publication Data
ISBN 978-1-119-28332-4
Cover image: Downhole Logging, Aleksei Zakirov | Dreamstime.com
Cover design by Kris Hackerott
Set in size of 11pt and Minion Pro by Manila Typesetting Company, Makati, Philippines
2.2.5
2.2.7
2.2.8
2.2.9
2.2.10
2.3.3
2.3.5
2.3.3.1 Run No. 1.
2.3.3.2 Run No. 2.
2.3.4.4 Run No. 8. Flowline volume
2.3.4.5 Run No. 9. Time-varying flowline volume inputs from FT-07
and amplitude attenuation, anisotropic media with dip – detailed theory, model and numerical
2.3.5.2
2.3.6
3.1.1
Example DD-7. “Drawdown-only” data with multiple inverse scenarios for 0.1 md/cp application 168
2.3.6.5 Drawdown – buildup applications 173
Example DDBU-1. Drawdown-buildup, high overbalance 173
Example DDBU-2. Drawdown-buildup, high overbalance 177
Example DDBU-3. Drawdown-buildup, high overbalance 180
Example DDBU-4. Drawdown-buildup, 1 md/cp calculations 184
Example DDBU-5. Drawdown-buildup, 0.1md/cp calculations 188
2.3.8 Multiphase flow with inertial effects –Applications to borehole invasion, supercharging, clean-up and contamination
2.3.8.1
2.3.8.2
3.2
3.4
3.5
3.6
3.7
Example 5-2. Cylindrical radial liquid displacement without cake
Example 5-3. Spherical radial liquid displacement without
Example 5-4. Lineal liquid displacement without mudcake, including compressible flow transients
Example 5-5. Von Neumann stability of implicit time schemes
Example 5-6. Gas displacement by liquid in lineal core without mudcake, including compressible flow transients
problem
Example 5-7. Simultaneous mudcake buildup and displacement front motion for incompressible
Preface
Formation testing, unlike conventional logging methods focused on resistivity, acoustic, nuclear or magnetic resonance approaches, provides direct results as opposed to indirect inferred properties. In sampling, actual in-situ fluids are collected for surface evaluation. And in pressure transient analysis, properties that pertain to production economics like mobility, compressibility, anisotropy and pore pressure are obtained directly from the underlying Darcy flow equations. By and large, the conventional subject matter deals with single, dual and multiprobe tools where pad nozzles are displaced axially relative to each other and along the same azimuth. This being so, idealized spherical “source” or “sink” methods are used in formulating forward and inverse problems.
Even so, few models have proven useful. An early steady model for spherical flow no longer applies to the lower mobility formations encountered in practice. Later transient models contain complicated Bessel functions and integrals whose effective use in the field is questionable. And then, a rapid, early-time prediction method for “effective permeability” and pore pressure, addressing the low mobility and “not so low” flowline volume limit – while significant in the 1990s and, in fact, invented by the last author, does not address all-important supercharging effects uncovered in recent field-based publications.
Fortunately, progress in source methods has been made, but at such an unusual pace that any presentations at industry meetings would have been rapidly dated. In support of our work, John Wiley & Sons has published our research in three volumes during 2014 – 2019, introducing the latest ideas and techniques to the industry, complete with derivations, equations and software. The present work, our latest formation testing addition to Wiley-Scrivener’s Petroleum Engineering Handbook Series, serves several purposes. While “handbooks” normally refer to summaries of decades-old technologies, this edition is timely because numerous new advances have been made in related and interdependent areas. These include pressure transient analysis, forward and inverse modeling, supercharge, mudcake
growth and fluid invasion formulations, and contamination and cleaning multiphase methods – and all during the past two decades by the present authors. While China Oilfield Services Limited (COSL) does manufacture its own conventional single and dual probe tools, it is the availability of our complete suite of software models that allows its tools to be used in many more innovative ways.
For example, methods are available to predict permeability and pore pressure rapidly from early time data in low mobility formations with strong flowline volume. But what if significant supercharging exists? Most inverse methods require constant flow rate drawdowns. What if this is not possible? And unacceptably, few authors have ever rigorously studied mudcake growth and fluid invasion, which produce the thick cakes responsible for stuck formation testers – the same phenomena associated with supercharge. Nor do they address the thin cakes that wreak havoc on nozzle pad sealing – leakages that would doom any formation testing job. Numerous related questions are treated in this comprehensive volume. And so this handbook, which addresses all of these problems from source model perspectives, provides unified discussions in forward and inverse formation testing analysis, supercharge in pressure evolution and permeability prediction, plus related topics in fluid invasion, mudcake growth and displacement front prediction. It is our hope that this work stimulates continuing research and enhances the innovative use of conventional tools in the field.
During the past several years, other high risk research and development projects were undertaken at COSL. In the early 1990s, an innovative “multiprobe” formation tester was introduced by a major service company that has greatly benefited the industry. This tool, consisting of an active “sink probe” and a passive “horizontal” observation probe displaced at 180° azimuthally from the sink, would provide measurements for horizontal and vertical permeability. However, in low mobility applications, measured pressure drops at the latter probe were often orders-of-magnitude less than those obtained at the pumping probe. This limitation attracted the interests of COSL engineers, who raised several unusual design challenges. “What if three azimuthally displaced probes, each separated by 120° from the others, were used?” And further, “What if each probe in the triple multiprobe tool were capable of operating independently from the others?”
What would be the logging advantages? What additional parameters of formation evaluation interest could we predict? Is it possible to detect heterogeneities? Dip angle? Can we pump at high rates without releasing dissolved gas? In order to design such a multiprobe tool, a fully three-dimensional transient model would be required to guide mechanical design
Preface xv
as well as to support interpretation procedures at the rigsite. Can a rapid, stable, accurate and easy-to-use computational method be devised? Is it possible to develop a robust procedure that supports field work in horizontal and vertical mobility definition? How would we apply “big data” statistical approaches using advanced algorithms? Can inverse procedures be solved accurately and rapidly at the rigsite and in field offices?
These questions are addressed in a companion 2021 volume in John Wiley’s Advances in Petroleum Engineering series, entitled Multiprobe Pressure Analysis and Interpretation, by Tao Lu, Minggao Zhou, Yongren Feng, Yuqing Yang and Wilson Chin. This complementary volume contains math models entirely different from the present, but which are also applicable to conventional 180° dual probe tools. Both of our 2021 books, drawing on research and engineering developed over more than a decade, are essential to modern formation testing, and we hope that both will find permanent places on petroleum engineers’ bookshelves. In this time of great uncertainty, one truth prevails: now, more than ever, innovation is needed to explore and produce natural resources more efficiently. And innovation in engineering means nothing less than a thorough understanding of physics and mathematics and putting both to important practical use.
The Authors, Beijing and Houston
Acknowledgements
The authors wish to thank the management of China Oilfield Services Limited (COSL) for permission to publish this manuscript. Our research efforts hope to advance formation testing, algorithm design and well logging technology and bring greater efficiencies to exploration and production. We are also indebted to Xiaoying Zhuang for her interpretation and translation skills, and usual hard work and perseverance, which have been instrumental in communicating a wide range of engineering and technical ideas to English-speaking audiences over the past decade. And last but not least, we again thank Phil Carmical, Acquisitions Editor and Publisher, for his confidence and faith in our research activities. In times of economic uncertainty such as ours, it is imperative that “the show must go on” and oil and gas industry professionals continue to “push the envelope” despite the headwinds. This monograph describes our persistent and continuing efforts in this endeavor and we are pleased to present our ideas to our petroleum engineering colleagues.
1
Pressure Transient Analysis and Sampling in Formation Testing
The formation tester is a well logging instrument with extendable pad nozzles which, when pressed against the borehole sandface, extracts in situ formation fluids for delivery to the surface for chemical examination. This process characterizes its fluid “sampling” function. By-products of this operation are pressure transient histories, which can be interrogated using Darcy math models for fluid and formation properties such as permeability, mobility, anisotropy, compressibility and pore pressure. This is referred to as “pressure transient analysis,” or simply, “PTA.” Both can be conducted as wireline or Measurement While Drilling, or “MWD,” applications, where these operations now represent invaluable elements of the standard well logging suite.
Pressure transient analysis challenges. While collecting and transporting fluids is relatively straightforward, e.g., storing samples in secure vessels that maintain downhole conditions, the PTA process poses a greater design challenge. A well designed tool often begins with a good understanding of the environment, plus physics coupled with sound experience in mathematical modeling. Some ideas are obvious. For example, a single “source” or “sink” probe, serving both pumping and pressure observation functions, will at most provide the “spherical permeability” kh2/3kv/1/3, where kh and kv are horizontal and vertical permeabilities. Thus, “single probe” tools, while mechanically simple, will offer fewer logging advantages than “dual probe” or “multiprobe tools” which provide much greater formation evaluation information.
2 Supercharge, Invasion and Mudcake Growth
Figure 1.1. Drawdown-buildup pressure response with dynamic pumping action and flowline.
But how are probe arrays configured and placed for optimal effect?
Figures 1.1 and 1.2 illustrate the operation of a single probe tool that withdraws fluid and then stops, creating the expected “drawdown and buildup” shown. If a second probe is desired, should it be placed an axial distance apart but along the same azimuth? Or azimuthally apart, at 180o away along the borehole circumference? What about a “drawdown only” pumpout? Or perhaps, have the pump oscillate sinusoidally in place, thus mimicking the AC transmissions of an electromagnetic logging tool? How many probes are best? What are their flow areas? Do answers to these questions depend on fluid and formation properties?
Figure 1.2. Downhole, surface and logging truck operations.
Background development. The present book addresses these questions for “source” or “sink models” of the pumping nozzle, these terms referring to ideal representations of the flow where borehole and pad geometry are described using mathematically small closed surfaces. The recent books due to Chin et al. (2014) or Formation Testing: Pressure Transient and Contamination Analysis, Chin et al. (2015) or Formation Testing: Low Mobility Pressure Transient Analysis, and Chin (2019) or Formation Testing: Supercharge, Pressure Testing and Contamination Models, published by John Wiley & Sons, contain complete math derivations and detailed validations. However, the rapid pace of recent development suggests a separate volume in Wiley’s Handbook of Petroleum Engineering Series, focused on the main ideas
4 Supercharge, Invasion and Mudcake Growth behind the recent works. These ideas are essential as they are also used in the design of newer COSL formation testing tools as well as in interpretation software now available to the petroleum industry. What engineers lack, at present, are job planning and PTA tools both useful at the rigsite and at engineers’ desktops. It is our purpose to support this pressing need.
Figure 1.3. Recent formation testing book publications.
1.1 Conventional Formation Testing Concepts.
Formation testing design concepts are rich and varied. A pumping probe, operating as a “sink” or (equivalently) a “source,” or both, also tracks pressure transient responses. Other pressure probes my reside along the tool body, displaced axially, azimuthally or both, which may actively pump or act as passive observers. While the primary formation tester function is fluid sampling, where in-situ reservoir fluids are collected and transported to the surface for analysis, pressure measurements represent critical by-products important to formation evaluation. Examples of testers offered by different manufacturers for wireline and MWD applications are given in Figures 1.4 – 1.7.
In a “handbook” such as this, it is important to provide examples of prototypes, commercial tools and systems. The wide ranges in design parameters can be surprising to newcomers in formation testing. For example, the “vertical and sink probes” in Figure 1.6, which are displaced axially but lie along the same azimuth, can range from six or seven inches to as much as 2.3 ft (27.6 in) and 10.3 ft (123.6 in), where the latter two distances are obtained from the manufacturer’s figure in SPE Paper No. 36176. We might, for example, ask, “Just what does the distant observation probe “see” under different mobility backgrounds?” “Will the tool do the job for my formation?” This book attempts to answer the most obvious questions, but it also aims at providing the tools and software for readers to address those pressing questions that invariably arise in any new logging scenario. To provide a flavor of how hardware literature and specifications might appear, we have included discussion of COSL material related to its standard product lines. Note that COSL’s new “triple probe, 120o tool” (as opposed to a conventional 180o tool) is treated separately in our companion 2021 book.
Figure 1.6. Conventional dual and triple probe testers.
Figure 1.7. Dual probe tester with dual packer.
Pressure Transient Analysis and Sampling 7
Close-ups of early single and dual probe prototype formation testers are shown in Figure 1.8. These photographs were obtained during field tests. The black pads shown perform an important sealing function, which prevents leakage of fluid through its contact surface with the sandface. However, they are not as “simple” as they appear. For instance, at any given pump rate, the pressure drop, which depends on nozzle diameter, may be excessive and allow the undesired release of dissolved gas – orifice sizes must be chosen judiciously, as suggested by the wide variety of choices shown in Figure 1.9. The shape of the hole or slot is also important; circular or oval shapes may be acceptable for consolidated matrix rock, but slotted models may be required for naturally fractured media or unconsolidated formations. Of course, in supporting PTA interpretation objectives, the size and shape of a formation tester’s pads must be incorporated into the host math model. More often than not, the model must be simple and mathematically tractable in order to obtain useful answers in a reasonable amount of time. This may require the use of idealized source or sink models, or numerical models with limited numbers of grids in the case of finite difference or finite modeling – consequently, questions related to calibration or geometric factors arise, along with test procedures, etc.
Figure 1.8. Early COSL single and dual probe prototype formation testers (details in 2014 and 2015 books).
Figure 1.9. COSL pad designs with varied sizes and shapes, for different applications, e.g., firm matrix rock, unconsolidated formations, fractured media, and so on..
Pressures obtained in PTA logging are used for multiple applications. For example, depending on the tool, permeability, anisotropy, compressibility and pore pressure are all possible (the term “mobility,” defined as the ratio of permeability to viscosity, is often interchangeably used, assuming that the viscosity is known). The pore pressure itself is used to identify fluids by their vertical hydrostatic gradients; this is possible because changes in pressure are affected by changes in fluid density. Sudden changes in pressure, for instance, may indicate the presence of barriers. However, the raw measured pressure, unless corrected for the “cushioning” effects associated with flowline volume, will not reflect pore pressures accurately. The correction depends, in turn, on the line volume as well as the compressibility and the mobility of the formation fluid. All said, the physics and math can be challenging, but solutions and analy tical highlights are presented in the next chapter for a wide variety of tools and applications. Chapter 2 provides a broad state-of-the-art review for source and sink models.
The “Enhanced Formation Dynamic Tester” is an advanced wireline formation testing system that delivers: (1) Multiple, large-volume highpurity formation fluid samples with downhole fluid characterization, (2) Reliable formation pressure testing, and (3) Real-time downhole fluid analyze, and more. Typical tool string configurations and architectures are shown in Figures 1.10 and 1.11. For detailed specifications, the reader is referred to the latest updated manufacturer’s literature.
COSL’s EFDT is designed to obtain formation pressures and formation fluid samples at discrete depths within a reservoir. Analyzing pressure buildup profile and the properties of fluid samples helps provide a more complete description of reservoir fluids and behavior. The EFDT service provides key petrophysical information to determine the reservoir volume, producibility of a formation, type and composition of the movable fluids, and to predict reservoir behavior during production.
THE EFDT is a modular formation testing system. It can be customized for the specialized applications. The modularity of EFDT ensures its ability to test and sample fluids in a wide range of geological environments and borehole conditions. For its basic configuration, the string includes a fully controllable Dual Probe Module for fluid intaking, a Flow Pump Module for variable-volume drawdown and pump out of contaminated fluids, a Fluid Sensor Module for dynamic properties of fluids, a PVT Carrier Module for monophase sampling, and a Large Sample Carrier Module for large-volume normal sampling. It can also be configured with a Straddle Packer Module, an Optical Analysis Module, a Focused Probe Module and a Multi-PVT Tank Module to meet the requirements of complex reservoir formation tests, such as low permeability rock or natural fractures.
